Effective Range Parameters Research Articles

Low-Energy Theorems for Neutron–Proton Scattering in χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi $$\\end{document}EFT Using a Perturbative Power Counting

Low-energy theorems (LETs) for effective-range parameters in nucleon-nucleon scattering encode properties of the long-range part of the nuclear force. We compute LETs for S-wave neutron–proton scattering using chiral effective field theory with a modified version of Weinberg power counting. Corrections to the leading order amplitude are included in distorted-wave perturbation theory and we incorporate contributions up to the third order in the power counting. We find that LETs in the 1S0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^1S_0$$\\end{document} and 3S1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3S_1$$\\end{document} partial waves agree well with empirical effective-range parameters. At the same time, phase shifts up to laboratory scattering energies of about 100 MeV can be reproduced. We show that it is important to consider the pion mass splitting in the one-pion exchange potential in the 1S0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^1S_0$$\\end{document} partial wave while the effect is negligible in the 3S1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3S_1$$\\end{document} partial wave. We conclude that pion exchanges, as treated in this power counting, accurately describe the long-range part of the S-wave nuclear interaction.

Interactions of omega mesons in nuclear matter and with nuclei

In-medium interactions of omega -mesons in infinite nuclear matter and finite nuclei are investigated in a microscopic approach, focused on the particle-hole excitations of the medium involving nucleonic NN^{-1} and N^*N^{-1} modes, where N^* denotes a nucleon resonance. The nuclear polarization tensors include relativistic mean-field dynamics by self–consistent scalar and vector fields. The resulting self-energies are transmitted to finite nuclei in local density approximation. Real and imaginary parts of longitudinal and transversal self-energies are discussed. The relation of the present approach to meson cloud models is addressed and an ambiguity is pointed out. Applications to recent data on the in–medium width of omega mesons scattered on a Niobium target serve to determine unknown N^*Nomega in-medium coupling constants. The data are well described by N^*N^{-1} self–energies containing S–wave and P-wave N^* resonances. Exploratory investigations, however, show that the spectroscopic composition of self-energies depends crucially on the near-threshold properties of the width which at present is known only within large error bars. The calculations predict the prevalence of transversal self–energies, implying that vector current conservation is still maintained in the nuclear medium by slightly more than 90%. Schrödinger-equivalent potentials are derived and scattering lengths and effective range parameters are extracted for the longitudinal and transversal channel. Longitudinal and transversal spectral distributions are discussed and the dependencies on momentum and nuclear density are investigated. Schrödinger-type omega +{}^{93}Nb optical potentials are constructed. Low-energy parameters are determined, are used to study the pole structure of the S-matrix at threshold. The effective range expansion of the omega-nucleus K-matrix led to a omega +{}^{93}Nb bound states with binding energy Re(varepsilon _B)=-448 keV but of width Gamma _B=4445 keV.

Bayesian estimation of the low-energy constants up to fourth order in the nucleon-nucleon sector of chiral effective field theory

We use Bayesian methods and Hamiltonian Monte Carlo (HMC) sampling to infer the posterior probability density function (PDF) for the low-energy constants (LECs) up to next-to-next-to-next-to-leading order (N3LO) in a chiral effective field theory ($\ensuremath{\chi}\mathrm{EFT}$) description of the nucleon-nucleon interaction. In a first step, we condition the inference on neutron-proton and proton-proton scattering data and account for uncorrelated $\ensuremath{\chi}\mathrm{EFT}$ truncation errors. We demonstrate how to successfully sample the 31-dimensional space of LECs at N3LO using a revised HMC inference protocol. In a second step we extend the analysis by means of importance sampling and an empirical determination of the neutron-neutron scattering length to infer the posterior PDF for the leading charge-dependent contact LEC in the $^{1}S_{0}$ neutron-neutron interaction channel. While doing so we account for the $\ensuremath{\chi}\mathrm{EFT}$ truncation error via a conjugate prior. We use the resulting posterior PDF to sample the posterior predictive distributions for the effective range parameters in the $^{1}S_{0}$ wave as well as the strengths of charge-symmetry breaking and charge-independence breaking. We conclude that empirical point-estimate results of isospin breaking in the $^{1}S_{0}$ channel are consistent with the PDFs obtained in our Bayesian analysis and that, when accounting for $\ensuremath{\chi}\mathrm{EFT}$ truncation errors, one must go to next-to-next-to-leading order to confidently detect isospin breaking effects.

Measurement of the [formula omitted] neutron-neutron effective range in neutron-deuteron breakup

We report the most precise determination of the S01 neutron-neutron effective range parameter (rnn) from neutron-neutron quasifree scattering in neutron-deuteron breakup. The experiment setup utilized a collimated beam of 15.5 MeV neutrons and an array of eight neutron detectors positioned at angles sensitive to several quasifree scattering kinematic configurations. The two neutrons emitted from the breakup reaction were detected in coincidence and time-of-flight techniques were used to determine their energies. The beam-target luminosity was measured in-situ with the yields from neutron-deuteron elastic scattering. Rigorous Faddeev-type calculations using the CD Bonn nucleon-nucleon potential were fit to our cross-section data to determine the value of rnn. The analysis was repeated using a semilocal momentum-space regularized N4LO+ chiral interaction potential. We obtained values of rnn=2.86±0.01(stat)±0.10(sys) fm and rnn=2.87±0.01(stat)±0.10(sys) fm using the CD Bonn and N4LO+ potentials, respectively. Our results are consistent with charge symmetry and previously reported values of rnn.

Effective field theory analysis of 3He–α scattering data

We treat low-energy 3He–α elastic scattering in an effective field theory (EFT) that exploits the separation of scales in this reaction. We compute the amplitude up to next-to-next-to-leading order, developing a hierarchy of the effective-range parameters (ERPs) that contribute at various orders. We use the resulting formalism to analyse data for recent measurements at center-of-mass energies of 0.38–3.12 MeV using the scattering of nuclei in inverse kinematics (SONIK) gas target at TRIUMF as well as older data in this energy regime. We employ a likelihood function that incorporates the theoretical uncertainty due to truncation of the EFT and use Markov chain Monte Carlo sampling to obtain the resulting posterior probability distribution. We find that the inclusion of a small amount of data on the analysing power A y is crucial to determine the sign of the p-wave splitting in such an analysis. The combination of A y and SONIK data constrains all ERPs up to O(p 4) in both s- and p-waves quite well. The asymptotic normalisation coefficients and s-wave scattering length are consistent with a recent EFT analysis of the capture reaction 3He(α, γ)7Be.

Femtoscopy of the J/ψ-nucleon interaction

I discuss the prospects of using femtoscopy in high-energy protonproton and heavy-ion collisions to learn about the low-energy J/ψ-nucleon interaction. Femtoscopy is a technique that makes it possible to obtain spatiotemporal information on particle production sources at the femtometer scale through measurements of two-hadron momentum correlation functions. These correlation functions also provide information on low-energy hadron-hadron forces as final-state effects. In particular, such correlation functions give access to the forward scattering amplitude. One can express the forward amplitude as the product of the J/ψ chromopolarizability and the nucleon’s average chromoelectric gluon distribution, the latter being relevant to the problem of the origin of the nucleon mass. I will present the results of a recent study using the information on the J/ψ-nucleon interaction from lattice QCD simulations to compute J/ψ-nucleon correlation functions. The calculated correlation functions show clear sensitivity to the final-state interaction. I conclude discussing open issues regarding the use of the effective range expansion formula to fit experimental data for small scattering lengths and large effective range parameters.

Recombination in the universal four-fermion system

In the systems of spin 12 fermions with resonant S-wave interactions supporting only weakly bound dimers the antisymmetry forbids recombination of three (or more) fermions at zero energy. However, the fermion-fermion-dimer recombination is only partially suppressed. It is studied in the framework of momentum-space integral equations for the four-particle transition operators. In the vicinity of the unitary limit the fermion-fermion-dimer recombination rate, rescaled to build dimensionless quantity, is found to be linear in the effective range parameter, enabling a simple and accurate parametrization as well as evaluation of finite-range effects for any potential model. This feature makes the present results very useful in benchmarking different methods for three-cluster breakup and recombination calculations in four-particle systems. The interplay of the three-fermion and fermion-fermion-dimer recombination processes and their consequences for ultracold mixtures of fermions and dimers is discussed.

A Region-Specific Ground-Motion Model for Inelastic Spectral Displacement in Northern Italy Considering Spatial Correlation Properties

Abstract The peak inelastic displacement of single-degree-of-freedom bilinear systems (Sdi) is an effective intensity measure linking ground-motion features to the inelastic response and subsequent structural and nonstructural damage of engineered systems. This study develops a region-specific ground-motion model for Sdi considering source, path, and site effects and explicitly accounting for the spatial correlation between intraevent residuals when the model parameters are estimated. The model is developed based on 2427 two-component horizontal ground-motion records from 85 events in northern Italy with magnitudes ranging from 4.0 to 6.4 and source-to-site distances less than 200 km. An exponential stationary and isotropic model is considered to represent the spatial correlation properties of Sdi (after scrutinizing the appropriateness of the underlying assumptions for such a model). Comparisons are performed with existing models in the literature in terms of Sdi estimates, as well as the (spatial correlation) effective range parameter. Two practical applications of the developed model are presented: one on estimating the spatial distribution of Sdi (as an essential ingredient for seismic loss assessments) and one on the engineering validation of region-specific ground-motion simulations. Challenges regarding such validations are also discussed.

Elastic α−C12 scattering at low energies with the sharp resonant 03+ state of O16

An inclusion of sharp resonant $0_3^+$ state of $^{16}$O and first excited $2_1^+$ state of $^{12}$C in a study of $s$-wave elastic $\alpha$-$^{12}$C scattering at low energies is investigated in an effective Lagrangian approach. The elastic scattering amplitude is parted into two; one is for the sharp resonant $0_3^+$ state of $^{16}$O parameterized by Breit-Wigner formula, and the other is for a non-resonant part of the amplitude parameterized by effective range expansion. In the non-resonant part of the amplitude, a contribution from the $2_1^+$ state of $^{12}$C is included. We discuss a large correlation between a coupling for the $2_1^+$ state of $^{12}$C and an effective range parameter $Q_0$ as well as a necessity of inclusion of a vertex correction for the initial and final $\alpha$-$^{12}$C states. After fixing parameters appearing in the amplitudes by using experimental data, we calculate asymptotic normalization coefficients for ground $0_1^+$ state and first excited $0_2^+$ state of $^{16}$O and compare them to previous results found in literature.

Correlation properties of integral ground‐motion intensity measures from Italian strong‐motion records

SummaryThis study investigates the correlation properties of integral ground‐motion intensity measures (IMs) from Italian strong‐motion records. The considered integral IMs include 5–95% significant duration, Housner intensity, cumulative absolute velocity, and Arias intensity. Both IM spatial correlation and the correlation between different integral and amplitude‐based IMs (i.e., cross‐IM correlation) are addressed in this study. To this aim, a new Italian ground‐motion model (GMM) with spatial correlation for integral IMs is first introduced. Based on the newly developed GMM, the empirical correlation coefficients from interevent and intraevent residuals are investigated and various analytical correlation models between integral IMs and amplitude‐based IMs are proposed. The effective range parameter representing spatial correlation properties and the trend in the cross‐IM correlations are compared with existing models in the literature. The variability of the effective range parameters with respect to event‐specific features is also discussed. Modeling ground‐motion spatial and cross‐IM correlations is an important step in seismic hazard and risk assessment of spatially distributed systems. Investigating region‐specific correlation properties based on Italian strong‐motion records is of special interest as several correlation models have been developed based on global datasets, often lacking earthquakes in extensional regions such as Italy.

Exploring the unknown Lambda-neutron interaction

No published \LambdaΛn scattering data exist. A relativistic heavy-ion experiment has suggested that a \LambdaΛnn bound state was seen. However, several theoretical analyses have cast serious doubt on the bound-state assertion. Nevertheless, there could exist a three-body \LambdaΛnn resonance. Such a resonance could be used to constrain the \LambdaΛn interaction. We discuss \LambdaΛnn calculations using nn and \LambdaΛn pairwise interactions of rank-one, separable form that fit effective range parameters of the nn system and those hypothesized for the as yet unobserved \LambdaΛn system based upon four different \LambdaΛN potentials. The use of rank-one separable potentials allows one to analytically continue the \LambdaΛnn Faddeev equations onto the second complex energy plane in search of resonance poles, by examining the eigenvalue spectrum of the kernel of the Faddeev equations. Although each of the potential models predicts a \LambdaΛnn sub-threshold resonance pole, scaling of the \LambdaΛn interaction by as little as \sim∼5% does produce a physical resonance. This suggests that one may use photo-(electro-)production of the \LambdaΛnn system from tritium as a tool to examine the strength of the \LambdaΛn interaction.

Low-energy bound states, resonances, and scattering of light ions

We describe bound states, resonances and elastic scattering of light ions using a $\delta$-shell potential. Focusing on low-energy data such as energies of bound states and resonances, charge radii, asymptotic normalization coefficients, effective-range parameters, and phase shifts, we adjust the two parameters of the potential to some of these observables and make predictions for the nuclear systems $d+\alpha$, $\mbox{$^3$He}+\alpha$, $\mbox{$^3$He}+\alpha$, $\alpha+\alpha$, and $p+\mbox{$^{16}$O}$. We identify relevant momentum scales for Coulomb halo nuclei and propose how to apply systematic corrections to the potentials. This allows us to quantify statistical and systematic uncertainties. We present a constructive criticism of Coulomb halo effective field theory and compute the unknown charge radius of $^{17}$F.

Can a $$\varLambda nn$$ Resonance Constrain the $$\varLambda n$$ Amplitude?

We address the question of constraints on the $$\varLambda n$$ amplitude as a result of observing a $$\varLambda nn$$ resonance above the $$\varLambda nn$$ three-body threshold. To examine this question, we will first demonstrate that by starting with a $$\varLambda n$$ interaction based upon the experimental $$\varLambda p$$ data and then scaling the $$\varLambda n$$ potential by $$\approx 8\%$$ one can generate a $$\varLambda nn$$ resonance, and with a sufficiently large scaling one can generate a $$\varLambda nn$$ bound state. This is achieved using the three-body Faddeev equations with rank one separable potentials for all pairwise interactions. The use of separable potentials is motivated by two factors: (i) the Faddeev equations reduce to a set of one dimensional integral equations that can be analytically continued into the complex energy plane where resonances reside. (ii) The $$\varLambda n$$ amplitude can be defined in terms of the effective range parameters. As a result we can explore the question: What constraint can be placed on the $$\varLambda n$$ effective range parameters by the $$\varLambda nn$$ resonance parameters?

Seismic Behavior Effect of Knee Braced Frames Considering Different Type of Geometry under Non-Linear Analysis

The design and behavior of a ductile structural system called a knee-braced moment frame are presented in this paper. The design of this structural system is based on a capacity-design concept that results in ductile behavior. The knee part is a fuse-like component that dissipates energy by the formation of plastic flexural and/or shear hinges at its ends and mid-span, when the building is subjected to severe lateral loads. However, the diagonal brace component, on the other hand, provides the required level of lateral stiffness and remains in the elastic range without buckling at any time. Attempts have been made, in the present study, to investigate the non-linear seismic behavior of Knee-Braced Frame systems for various influencing factors, and to formulate the effects of the number of building stories, the length of the knee element, and moment of inertia of the bending members on the seismic behavior, the drift of the stories, and the failure mode of these systems. Finally, based on the results of the study, some recommendations have been offered for the effective range parameters for the optimal performance of these systems.

Dimensional crossover in non-relativistic effective field theory

Isotropic scattering in various spatial dimensions is considered for arbitrary finite-range potentials using non-relativistic effective field theory. With periodic boundary conditions, compactifications from a box to a plane and to a wire, and from a plane to a wire, are considered by matching S-matrix elements. The problem is greatly simplified by regulating the ultraviolet divergences using dimensional regularization with minimal subtraction. General relations among (all) effective-range parameters in the various dimensions are derived, and the dependence of bound states on changing dimensionality are considered. Generally, it is found that compactification binds the two-body system, even if the uncompactified system is unbound. For instance, compactification from a box to a plane gives rise to a bound state with binding momentum given by in units of the inverse compactification length. This binding momentum is universal in the sense that it does not depend on the two-body interaction in the box. When the two-body system in the box is at unitarity, the S-matrices of the compactified two-body system on the plane and on the wire are given exactly as universal functions of the compactification length.

Elastic α−C12 scattering at low energies with the bound states of O16 in effective field theory

The elastic $\alpha$-$^{12}$C scattering for $l=0,1,2,3$ channels at low energies is studied, including the energies of excited bound states of $^{16}$O, in effective field theory. We introduce a new renormalization method due to the large suppression factor produced by the Coulomb interaction when fitting the effective range parameters to the phase sift data. After fitting the parameters, we calculate asymptotic normalization constants of the $0_2^+$, $1_1^-$, $2_1^+$, $3_1^-$ states of $^{16}$O. We also discuss the uncertainties of the present study when the amplitudes are interpolated to the stellar energy region of the $^{12}$C($\alpha$,$\gamma$)$^{16}$O reaction.

Mixed mode fatigue crack growth behavior of Ni-Cr-Mo-V high strength steel weldments

The extensive use of Ni-Cr-Mo-V high strength steels in modern marine environment poses increasing requirements for accurate characterization of the fatigue crack growth (FCG) behavior of their welded joints. The present work reported a study on a new generation Ni-Cr-Mo-V high strength steel concerning the mixed mode FCG behavior of its welded joint. Effects of microstructure and welding residual stresses (WRSs) were emphasized. It was found that the 4% compliance offset criterion in the conventional ASTM procedure and the 10% offset criterion in the normalized ASTM procedure were suitable for determination of the crack opening force of high strength steel weldments. A new effective stress intensity factor range parameter as the crack growth driving force was proposed, which yielded fairly good correlation for the mixed mode FCG data. Acicular ferrite with basket-weave microstructure in the weld metal exhibited favorable crack growth resistance relative to the base material and was preferred to the welded joints. The attained master or intrinsic FCG curves for the base material and the weld metal on the basis of the proposed parameter provided a basic database for the design of high strength steels employed in modern marine structures.

Effective-range parameters and vertex constants for Λ-nuclear systems

For a wide range of the core-nuclei ([Formula: see text]), the scattering lengths, effective radii, and the other effective-range parameters (up to the order [Formula: see text]) for the angular momentum [Formula: see text] are calculated within a two-body [Formula: see text]-model. For the same hypernuclear systems, the [Formula: see text]-matrix residues as well as the corresponding Nuclear-Vertex and Asymptotic-Normalization constants (NVC’s and ANC’s) for the bound states are also found.

Universality in the Neutron– $$^{\mathbf {19}}$$ 19 C Scattering Using Finite-Range Separable Interactions

We report a study on the low-energy properties of the elastic $s-$wave scattering of a neutron ($n$) in the carbon isotope $^{19}$C near the critical condition for the occurrence of an excited Efimov state in the three-body $n-n-^{18}$C system. For the separation energy of the two halo neutrons in $^{20}$C we use the available experimental data. We also investigate to which extent the universal scaling laws, strictly valid in the zero-range limit, will survive when using finite-range interactions. By allowing to vary the $n-^{18}$C binding energy, a scaling behavior for the real and imaginary parts of the $s-$wave phase-shift $\delta_0$ is verified, emerging some universal characteristics given by the pole-position of $k\cot(\delta_0^R)$ and effective-range parameters.

Research at the University of Kentucky Accelerator Laboratory

The Department of Physics and Astronomy at the University of Kentucky operates a 7-MV CN Van de Graaff accelerator that produces primary beams of protons, deuterons, and helium ions. An in-terminal pulsing and bunching system operates at 1.875MHz and is capable of providing 1ns beam bunches at an average current of several microamperes. Nearly all ongoing research programs involve secondary pulsed neutrons produced with gas cells containing deuterium or tritium, as well as with a variety of solid targets. Most experiments are performed at a target station positioned over a deep pit, so as to reduce the background created by backscattered neutrons. Recent experiments will be described; these include: measurements of n-p scattering total cross sections from En= 90 to 1800 keV to determine the n-p effective range parameter; the response of the plastic scintillator BC-418 below 1 MeV to low-energy recoil protons; n-p radiative capture cross sections important for our understanding of nucleosynthesis approximately 2minutes after the occurrence of the Big Bang; γ-ray spectroscopy following inelastic neutron scattering to study nuclear structure relevant to double-β decay and to understand the role of phonon-coupled excitations in weakly deformed nuclei; and measurements of neutron elastic and inelastic scattering cross sections for nuclei that are important for energy production and for our global understanding of the interaction of neutrons with matter.